Questions tagged [nonabelian-cohomology]
The nonabelian-cohomology tag has no usage guidance.
8 questions with no upvoted or accepted answers
12
votes
0
answers
272
views
sequences in non-abelian group cohomology
In general, if we have a (pro-)finite group $G$ and a sequence of (continuous) non-abelian $G$-modules $$1\rightarrow A\rightarrow B\rightarrow C\rightarrow 0,$$ such that the image of $A$ lies in the ...
- 273
10
votes
0
answers
347
views
The non-abelian Gauss-Manin connection; non-abelian M_dR; a Grothendieck lemma for cyrstals
I'm interested in understanding the non-abelian Gauss-Manin connection on Carlos Simpson's relative de Rham Moduli space $M_{dR}(X/S,n)$ for a smooth projective morphism of schemes $X/S$. The scheme $...
- 359
7
votes
0
answers
303
views
Albrecht Fröhlich's text `Groupoids, groupoid spaces and cohomology' (1965)
I am looking for Albrecht Fröhlich's unpublished text `Groupoids, groupoid spaces and cohomology' (1965). In this text Fröhlich defines cohomology of a group with coefficients in a groupoid (this was ...
- 14.2k
5
votes
0
answers
254
views
How can one concretely approximate a homotopy type by a scheme or (higher/derived) stack?
What methods are there to approximate an arbitrary homotopy type by an algebraic-geometric object in a concrete (read: computable) way?
I know this is an ambitious question, so maybe I should ...
- 1,635
3
votes
0
answers
308
views
Non-abelian group cohomology, additional information
Let $G$ be a (profinite) group, and let $M$ be a non-abelian $G$-module.
We know how to construct reasonably $H^0(G,M)$ and $H^1(G,M)$ and it turns out that $H^1(G,M)$ is just a pointed set and not ...
- 463
3
votes
0
answers
65
views
Connection on 3-bundle given as triplet of forms
A connection on a bundle is given locally by a Lie algebra-valued 1-form.
Gauge transformations act in the usual way on the forms, and form a groupoid.
A connection on a 2-bundle is given locally by ...
- 2,129
1
vote
0
answers
42
views
When is $B^G\backslash(B/A)^G$ finite?
Let $G$ be a locally compact group, let $A,B$ be (not necessarily abelian) connected reductive complex groups equipped with continuous actions of $G$ via algebraic automorphisms. Let $\phi:A\to B$ be ...
- 387
0
votes
0
answers
120
views
$G\cdot H$ with $G,H$ non-Abelian finite simple
Can a non-split extension of one non-Abelian finite simple group by another exist?
- 2,773